Deforming UV mesh by dragging vertex
LIVE UNWRAP!
Thanks to moonboots comment, looking up proportional editing and uv map made me find the video that introduced the technique I was talking about: https://www.youtube.com/watch?v=SXyIhYcYmoo
Turns out I needed to have Live Unwrap checked and transform my pinned vertices on the EDGES of my unwrapped mesh.